Overview
- Is the first book to provide a solid bridge between algorithmic information theory and statistical mechanics
- Clarifies a new aspect of the notion of temperature as the compression rate of the values of all thermodynamic quantities
- Serves as an introduction both to algorithmic information theory and to the fundamental framework of equilibrium statistical mechanics
Part of the book series: SpringerBriefs in Mathematical Physics (BRIEFSMAPHY, volume 36)
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Table of contents (9 chapters)
Keywords
About this book
A simplification of the setting of AIT is the noiseless source coding in information theory. First, in the book, a statistical mechanical interpretation of the noiseless source coding scheme is introduced. It can be seen that the notions in statistical mechanics such as entropy, temperature, and thermal equilibrium are translated into the context of noiseless source coding in a natural manner.
Then, the framework of AIT is introduced. On this basis, the introduction of a statistical mechanical interpretation of AIT is begun. Namely, the notion of thermodynamic quantities, such as free energy, energy, and entropy, is introduced into AIT. In the interpretation, the temperature is shown to be equal to the partial randomness of the values of all these thermodynamic quantities, where the notion of partial randomness is a stronger representation of the compression rate measured by means of program-size complexity. Additionally, it is demonstrated that this situation holds for the temperature itself as a thermodynamic quantity. That is, for each of all the thermodynamic quantities above, the computability of its value at temperature T gives a sufficient condition for T to be a fixed point on partial randomness.
In this groundbreaking book, the current status of the interpretation from both mathematicaland physical points of view is reported. For example, a total statistical mechanical interpretation of AIT that actualizes a perfect correspondence to normal statistical mechanics can be developed by identifying a microcanonical ensemble in the framework of AIT. As a result, the statistical mechanical meaning of the thermodynamic quantities of AIT is clarified. In the book, the close relationship of the interpretation to Landauer's principle is pointed out.
Authors and Affiliations
Bibliographic Information
Book Title: A Statistical Mechanical Interpretation of Algorithmic Information Theory
Authors: Kohtaro Tadaki
Series Title: SpringerBriefs in Mathematical Physics
DOI: https://doi.org/10.1007/978-981-15-0739-7
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2019
Softcover ISBN: 978-981-15-0738-0Published: 21 November 2019
eBook ISBN: 978-981-15-0739-7Published: 11 November 2019
Series ISSN: 2197-1757
Series E-ISSN: 2197-1765
Edition Number: 1
Number of Pages: XI, 136
Number of Illustrations: 1 b/w illustrations
Topics: Mathematical Physics, Algorithms, Data Structures and Information Theory, Statistical Physics and Dynamical Systems